Question

What is the degeneracy of the level of $H$-atom that has energy $\left(-\frac{R_{H}}{9}\right) ?$

• A. 16
• B. 9
• C. 4
• D. 1

Answer 1

Answer: (B)

Energy of the electron in the $n$th orbit in terms of $R_{ H }$ is
$E_{n}=-\frac{R_{ H } Z^{2}}{n^{2}}$
where, $Z=$ atomic number, $n^{2}=$ degeneracy
For H-atom, $E_{n}=-\frac{R_{ H }(1)^{2}}{n^{2}}$
$ -\frac{R_{ H }}{9} =-\frac{R_{ H }}{n^{2}} $
$\therefore n^{2} =9$